Model reduction: Why it is possible and how it can potentially help to control swarms of Unmanned Arial Vehicles (UAVs)

In many application areas, such as meteorology, traffic control, etc., it is desirable to employ swarms of Unmanned Arial Vehicles (UAVs) to provide us with a good picture of the changing situation and thus, to help us make better predictions (and make better decisions based on these predictions). To avoid duplication, interference, and collisions, UAVs must coordinate their trajectories. As a result, the optimal control of each of these UAVs should depend on the positions and velocities of all others - which makes the corresponding control problem very complicated. Since, in contrast to controlling a single UAV, the resulting problem is too complicated to expect an explicit solution, a natural idea is to extra expert rules and use fuzzy control methodology to translate these rules into a precise control strategy. However, with many possible combinations of variables, it is not possible to elicit that many rules. In this paper, we show that, in general, it is possible to use model reduction techniques to decrease the number of questions and thus, to make rules elicitation possible. In addition to general results, we also show that for the UAVs, optimal control indeed leads to a model reduction - and thus, to a drastic potential decrease in the corresponding number of questions.